Details

simplify34.9m

Calls

16516 calls:

Slowest
4.4s
(/ (* (* (* 3 3) 3) (* (* (* c c) c) (* (* a a) a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
4.4s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
3.7s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))
3.4s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))
3.2s
(/ (* (* (* c c) c) (* (* (* 3 a) (* 3 a)) (* 3 a))) (* (* (* 3 3) 3) (* (* a a) a)))

sample12.6m

Algorithm
72×intervals
Results
9.5m82064×body10240exit
54.3s33153×body1280valid
25.4s198514×body80valid
24.3s24490×body640valid
20.1s150895×body80nan
13.9s24944×body320valid
12.9s34925×body160valid
10.3s154039×pre80true
3.3s3128×body2560valid
1.5s7711×body160nan
1.2s4173×pre10240exit
317.0ms227×body5120valid

prune3.3m

series57.5s

Calls

427 calls:

Slowest
2.2s
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
870.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
779.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
665.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
662.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))

regimes11.5s

Accuracy

Total 20.2b remaining (8.3%)

3.1b0%Cubic critical, medium range
2.6b73.7%Quotient of products
2.4b23.5%Cubic critical, wide range
1.9b91.9%Cubic critical
1.7b0%Quadratic roots, wide range

rewrite9.8s

Algorithm
127×rewrite-expression-head
Calls

427 calls:

Slowest
279.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
277.0ms
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
267.0ms
(* (- (/ 1 (/ (/ v (- 1 m)) m)) 1) m)
187.0ms
(* (- (/ (* m (- 1 m)) v) 1) (- 1 m))
156.0ms
(* (- (/ m (/ v (- 1 m))) 1) m)
Rules
7962×*-un-lft-identity
7416×add-sqr-sqrt
6869×times-frac
5095×add-cube-cbrt
2764×add-exp-log
2733×prod-diff
1398×add-cbrt-cube
1303×pow1
1077×sqrt-prod
1070×prod-exp
965×difference-of-squares
949×div-exp
694×pow-exp
672×distribute-lft-out
671×associate-*r*
654×cbrt-prod
600×add-log-exp
595×associate-*l*
532×distribute-lft-out--
446×associate-/r*
437×expm1-log1p-u
427×log1p-expm1-u insert-posit16
394×associate-/r/
389×associate-/l*
387×div-inv
354×cbrt-unprod
346×pow-to-exp
319×distribute-rgt-in distribute-lft-in
304×frac-times
301×distribute-rgt-neg-in
300×fma-neg
294×cbrt-undiv
270×distribute-lft-neg-in
242×log-prod
239×flip--
238×flip3--
234×swap-sqr
213×pow-prod-down
203×unswap-sqr
194×difference-of-sqr-1
181×associate-*l/
172×associate-*r/
171×pow-prod-up
158×flip-+
157×flip3-+
149×1-exp
147×rec-exp
142×cbrt-div
122×fma-def
109×pow-sqr
106×tanh-def
97×pow-plus
89×neg-mul-1 *-commutative
86×sub-neg
84×frac-2neg clear-num log-pow
75×pow1/3
74×fma-udef
73×sqrt-pow1
70×pow2
67×diff-log
65×tan-quot
61×pow1/2
53×frac-sub associate-/l/
51×unpow-prod-down
50×associate--l+
47×exp-sum
44×pow-flip
38×associate--r+
37×rem-sqrt-square
34×exp-prod
33×sin-sum
29×rem-log-exp cos-sum
28×sqrt-div
26×log-div
24×sum-log
20×inv-pow
18×+-commutative
17×div-sub
13×neg-sub0
11×log1p-udef
10×log1p-expm1 pow3 neg-log
associate--l- pow-unpow
cos-mult
sqr-pow pow-pow rem-cbrt-cube acos-asin
associate-+l- rem-exp-log frac-add
associate--r-
expm1-udef exp-diff expm1-def
sqrt-unprod pow-div un-div-inv rem-square-sqrt sqr-cos
associate-+l+ expm1-log1p log-rec hypot-udef distribute-rgt-out-- cos-diff sin-mult
distribute-lft-neg-out distribute-frac-neg tanh-undef asin-acos acos-neg sin-diff unpow1/3

localize5.1s

bsearch1.5s

end1.0ms